The purpose of this research is to interpolate bipolarity into the definition vague soft set. This gives a new more applicable, flexible, and generalized extension set, fuzzy or even which bipolar In addition, types sets, as well some related concepts operations are established with examples. Moreover, properties sets including absorption, commutative, associative, distributive, De Morgan’s law...

We apply the classical theory of hyperrings to vague soft sets to derive the concepts of vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphism. The properties and structural characteristics of these concepts are also studied and discussed. Furthermore, the relationship between the concepts introduced here and the corresponding concepts in classical hyperring theor...

In this paper, we recall the concept of vague soft expert set theory and its operations. We define the AND and OR operations of vague soft expert set and some properties. We prove the De Morgan’s law on vague soft expert set. We then provide an illustrative example of vague soft expert set and its application in decision making.

In this paper, the dual hesitant fuzzy rough set (DHFRS) is studied from the viewpoint of assessment deviations. Firstly, according to the relationship between intuitionistic fuzzy set and vague set, the DHFRS is transferred into a fuzzy set, where the membership of any given element to it has multi-grouped values. By the idea of bootstrap sampling, a group of four sets are generated to describ...

In the construction process of smart grid, an assessment on primary equipments intelligent transformation is an urgent content in the first batch of intelligent substation pilot project. Wide investigation of intelligent substation pilot projects was conducted seriously in several regional power grids in China. An mathematical model was established to assess the substation primary equipments in...